NTCorrelation: Count-trefoil correlations

class treecorr.NTCorrelation(config=None, *, logger=None, **kwargs)[source]

Bases: BaseNZCorrelation

This class handles the calculation and storage of a 2-point count-trefoil correlation function, where a trefoil is any field with spin-3 rotational properties.

See the doc string of Corr3 for a description of how the triangles are binned along with the attributes related to the different binning options.

In addition to the attributes common to all Corr2 subclasses, objects of this class hold the following attributes:

Attributes:

  • xi – The correlation function, \(\xi(r) = \langle t_R\rangle\).

  • xi_im – The imaginary part of \(\xi(r)\).

  • varxi – An estimate of the variance of \(\xi\)

  • cov – An estimate of the full covariance matrix.

  • raw_xi – The raw value of xi, uncorrected by an RT calculation. cf. calculateXi

  • raw_xi_im – The raw value of xi_im, uncorrected by an RT calculation. cf. calculateXi

  • raw_varxi – The raw value of varxi, uncorrected by an RT calculation. cf. calculateXi

Note

The default method for estimating the variance and covariance attributes (varxi, and cov) is ‘shot’, which only includes the shape noise propagated into the final correlation. This does not include sample variance, so it is always an underestimate of the actual variance. To get better estimates, you need to set var_method to something else and use patches in the input catalog(s). cf. Covariance Estimates.

The typical usage pattern is as follows:

>>> nt = treecorr.NTCorrelation(config)
>>> nt.process(cat1,cat2)   # Compute the cross-correlation.
>>> nt.write(file_name)     # Write out to a file.
>>> xi = nt.xi              # Or access the correlation function directly.
Parameters:

  • config (dict) – A configuration dict that can be used to pass in kwargs if desired. This dict is allowed to have addition entries besides those listed in Corr2, which are ignored here. (default: None)

  • logger – If desired, a logger object for logging. (default: None, in which case one will be built according to the config dict’s verbose level.)

Keyword Arguments:

**kwargs – See the documentation for Corr2 for the list of allowed keyword arguments, which may be passed either directly or in the config dict.

calculateXi(*, rt=None)[source]

Calculate the correlation function possibly given another correlation function that uses random points for the foreground objects.

  • If rt is None, the simple correlation function \(\langle t_R\rangle\) is returned.

  • If rt is not None, then a compensated calculation is done: \(\langle t_R\rangle = (DT - RT)\), where DT represents the mean radial trefoil field around the data points and RT represents the mean radial trefoil field around random points.

After calling this function, the attributes xi, xi_im, varxi, and cov will correspond to the compensated values (if rt is provided). The raw, uncompensated values are available as rawxi, raw_xi_im, and raw_varxi.

Parameters:

rt (NTCorrelation) – The cross-correlation using random locations as the lenses (RT), if desired. (default: None)

Returns:

Tuple containing

  • xi = array of the real part of \(\xi(R)\)

  • xi_im = array of the imaginary part of \(\xi(R)\)

  • varxi = array of the variance estimates of the above values

finalize(vart)[source]

Finalize the calculation of the correlation function.

The Corr2.process_cross command accumulates values in each bin, so it can be called multiple times if appropriate. Afterwards, this command finishes the calculation by dividing each column by the total weight.

Parameters:

vart (float) – The variance per component of the trefoil field.

write(file_name, *, rt=None, file_type=None, precision=None, write_patch_results=False, write_cov=False)[source]

Write the correlation function to the file, file_name.

  • If rt is None, the simple correlation function \(\langle t_R\rangle\) is used.

  • If rt is not None, then a compensated calculation is done: \(\langle t_R\rangle = (DT - RT)\), where DT represents the mean trefoil field around the data points and RT represents the mean trefoil field around random points.

The output file will include the following columns:

Column

Description

r_nom

The nominal center of the bin in r

meanr

The mean value \(\langle r \rangle\) of pairs that fell into each bin

meanlogr

The mean value \(\langle \log(r) \rangle\) of pairs that fell into each bin

tR

The mean real part of the trefoil field relative to the center points.

tR_im

The mean imaginary part of the trefoil field relative to the center points.

sigma

The sqrt of the variance estimate of either of these

weight

The total weight contributing to each bin

npairs

The total number of pairs in each bin

If sep_units was given at construction, then the distances will all be in these units. Otherwise, they will be in either the same units as x,y,z (for flat or 3d coordinates) or radians (for spherical coordinates).

Parameters:

  • file_name (str) – The name of the file to write to.

  • rt (NTCorrelation) – The cross-correlation using random locations as the lenses (RT), if desired. (default: None)

  • file_type (str) – The type of file to write (‘ASCII’ or ‘FITS’). (default: determine the type automatically from the extension of file_name.)

  • precision (int) – For ASCII output catalogs, the desired precision. (default: 4; this value can also be given in the constructor in the config dict.)

  • write_patch_results (bool) – Whether to write the patch-based results as well. (default: False)

  • write_cov (bool) – Whether to write the covariance matrix as well. (default: False)